I've made the move to Monarch after getting domination or space race victories on the last 5 Prince games I've played.

How do you move beyond the early game? I've started and quit four games because of early impediments. For one, instead of wolves and lions, my warriors are destroyed by jaguars and bears. Second, early barbs aren't warriors, but a mix of warriors and archers; so my fog busting warriors are cut down by double combat promoted archers. I don't even want to know what kind of freebies the AI gets at Monarch level.

Should I still be doing the warrior > warrior > worker > settler pattern for first build that worked oh-so-well at Prince? Or should I crank out half a dozen warriors before I do anything else (which is what seems necessary)?

I can learn from the rest. Once I get in contact with multiple AIs, I learn well. But the years between start and say 800 BC ... well, I don't know what to be doing to survive long enough to encounter more than one or two other civs.

At Monarch the AI starts with a worker + the Archery tech.
If you start building a worker they are already busy producing a settler,
so you're always behind in expansion.
On huge maps + raging barbarians the AI expansion will slow down,
except Mali, because of the barbs. In one game the barbs captured/razed
21 AI cities. ( I always love to watch the replay to see how they were doing. :D )
Bronze Working, for Copper + Slavery, is a must. Archery also, if your
capital lacks copper, an exception will be the Incas. Fishing is also a must
if the start is coastal + seafood. The building order depends on the situation,
but I always skip the barracks if not Aggressive.

I play raging barbs, and it is fun to watch the AI sufer, especially if like me, you building the great wall, in one game, i reamined a city states (barbs really pile on the pressure after your second city), and waited until it was completed, the sent out my settlers with archer escorts, since the AI was so tentaive the best city spots were unused.

I recommend limiting early exploration, in most cases wait until your first warriro is killed, then just build archers in your capital, and then a worker then a settler, and prepare to expand outwards.

If you're particularly worried aout Barbs go as the Incas or the Persians, as Persia the worst the Barbs through at you (axeman) is mincemeat for the Immortal, and the Inca's UU holds off archers for a while.

You could always turn off Barbs as i used to do until i was confident enough to face the rough barbs.